Quantum phase transition of transition of light in coupled optical cavity arrays: A renormalization group study

We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons. We predict the quantum phase transition between the photonic Coulomb blocked induce Mott insulating phase and staggered order induced photonic insulating phase in the system due to the existence of two Rabi frequency oscillations. We also present the quantum phase transition from photonic superfluid phase to the photonic Mott insulating phase due to the presence of single Rabi frequency oscillation. We present the analytical derivation and physical analysis of the phase boundaries and the effect of detuning magnetic field. Our renormalization group calculation shows explicitly that for this system there is no self-duality. We also predict the Berezinskii-Kosterlitz-Thouless transition for the presence of single Rabi frequency oscillations.